Essential spectrum of Operators of Quantum Mechanics and Limit Operators

The talk is devoted to applications of the limit operators to the study of
essential spectra and exponential decay of eigenfunctions of the discrete
spectra for Schr\"{o}dinger and Dirac operators for wide classes of
potentials. Outline of the talk:

1) Fredholm property and location of the essential spectrum of systems of
partial differential operators with variable bounded coefficients;

2) Exponential estimates of solutions of systems of partial differential
operators with variable bounded coefficients;

3) Location of the essential spectrum of Schr\"{o}dinger and Dirac operators
and exponential estimates of eigenfunctions of the discrete spectrum.